The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

System Identification I

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

Thank you for reading stochastic processes and filtering theory. Maybe you have knowledge that, people have look numerous times for their favorite novels like this stochastic processes and filtering theory, but end up in harmful downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they are facing with some infectious bugs inside their computer. stochastic processes and filtering theory is available in our digital library an online access to it is set as public so you can download it instantly. Our digital library saves in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Merely said, the stochastic processes and filtering theory is universally compatible with any devices to read.

Stochastic Processes And Filtering Theory

The article reports an investigation on how to efficiently describe phase equilibrium in dynamic systems, and how to solve the resulting equations numerically. An overview of possible solution strategies is given. Different thermodynamic models are briefly reviewed, and important algorithms like PT flash are described. A flash tank with a mixture of propane and propylene is simulated to illustrate some different solution strategies.

https://www.mic-journal.no/PDF/1997/MIC-1997-2-4.pdf

Modelling and simulation of phase equilibrium in dynamic systems

Design of optimal operation and control of a run-of-river hydro power plant depends on good models for the elements of the plant. River reaches are often considered to be shallow channels with free surface flow. A typical model for such reaches thus use the Saint Venant model, which is a 1D model based on the mass and momentum balances. This combination of free surface and momentum balance makes the problem numerically challenging to solve. Here, the finite volume method with staggered grid is used to illustrate the dynamics of the river upstream from the Gronvollfoss run-of-river power plant in Telemark, Norway, operated by Skagerak Energi. A model of the same river in the Gronvollfoss power plant has been studied previously, but here the geometry of the river is changed due to new information from Skagerak Energi. The numerical scheme for solving the model has been further developed. In addition, the behavior of the dynamic model is compared to data from experiments, carried out on the Gronvollfoss run-of-river power plant. The essence of the experiments is to consider the time taken from an increase in the input volumetric flow, to a measured change in level in front of the dam at Gronvollfoss. The model is manual ly tuned by changin g the Strickler friction factor, the river length and the type of river slope/width (constant/varying) in order to fit the water level ahead of the Gronvollfoss dam from experimental data. Least squares model fitting is also used for the model with the constant slope and width of the river and this model shows good fitting after the manual tuning. The results of the improved model (numerically, tuned to experiments), is a model that can be further used for control synthesis and analysis.

/pdf/modeling-for-control-of-run-of-river-power-plant-pz916r4ze4.pdf

Modeling for control of run-of-river power plant Grønvollsfoss

The Czochralski (CZ) crystallization process is used to produce monocrystalline silicon for solar cell wafers and electronics. Tight temperature control of the molten silicon is most important for achieving high crystal quality. SINTEF Materials and Chemistry operates a CZ process. During one CZ batch, two pyrometers were used for temperature measurement. The silicon pyrometer measures the temperature of the molten silicon. This pyrometer is assumed to be accurate, but has much high-frequency measurement noise. The graphite pyrometer measures the temperature of a graphite material. This pyrometer has little measurement noise. There is quite a good correlation between the two pyrometer measurements. This paper presents a sensor fusion algorithm that merges the two pyrometer signals for producing a temperature estimate with little measurement noise, while having signicantly less phase lag than traditional lowpass

/pdf/a-sensor-fusion-algorithm-for-filtering-pyrometer-3noy00fxyx.pdf

A Sensor Fusion Algorithm for Filtering Pyrometer Measurement Noise in the Czochralski Crystallization Process

The two-phase drift flux model is extensively used in multiphase flow applications. In this study, we focus on possible numerical schemes for solving the drift flux model. Due to the complexity of the primitive equations and empirical parameters, it is challenging to achieve stability of the numerical scheme used for the drift flux model. The high resolution second order central scheme, the high resolution second order central-upwind scheme, and the high resolution third order and fifth order weighted essentially non-oscillatory schemes (WENO) were successfully implemented for the drift flux model. The schemes were tested with the shock tube discontinuity problem. The central-upwind-WENO scheme was developed and applied to the drift flux model. In the central-upwind-WENO scheme, the cell interface values were taken from the WENO reconstruction, and the monotone flux is calculated from the central-upwind flux. The central-upwind-WENO scheme can achieve higher order accuracy than the central-upwind scheme by using the same stencils which are used for the central-upwind scheme. The central-upwind-WENO scheme gives more accurate results than the central scheme, central-upwind scheme and the WENO scheme. Especially at the rarefaction and shock wave fronts, the central-upwind-WENO scheme gives sharper gradients compared to the other schemes. Instead of a limiter function, the central-upwind-WENO scheme uses a smoothness indicator. All the schemes used in the study are suitable for two-phase drift flux model simulation.

/pdf/development-of-central-upwind-weno-scheme-for-two-phase-1-d-tujokjts.pdf

Development of central-upwind-WENO scheme for two-phase 1-D drift-flux model

into monoethanolamine(MEA) by chemical absorption is presently the most favored method for the cap-ture of carbon dioxide from fossil fuel combustion. A benefit of chemical absorp-tion into amine solution is that at higher temperatures the chemical reaction can bereversed and the MEA recycled.The majority of previous work on amine CO

Bernt Lie

Papers

Modelling and simulation of phase equilibrium in dynamic systems

Modeling for control of run-of-river power plant Grønvollsfoss

A Sensor Fusion Algorithm for Filtering Pyrometer Measurement Noise in the Czochralski Crystallization Process

Development of central-upwind-WENO scheme for two-phase 1-D drift-flux model

A model for abatement of co2 emissions by de-absorption with monoethanolamine